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Self-consistent analytic solution for the current and the access resistance in open ion channels

D. G. Luchinsky1,2, R. Tindjong1, I. Kaufman3, P. V. E. McClintock1, and R. S. Eisenberg4

  • 1Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
  • 2Mission Critical Technologies Inc., 2041 Rosecrans Avenue, Suite 225, El Segundo, California 90245, USA
  • 3VNII for Metrological Service, Gosstandart, Moscow 119361, Russia
  • 4Department of Molecular Biophysics and Physiology, Rush Medical College, 1750 West Harrison, Chicago, Illinois 60612, USA

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Phys. Rev. E 80, 021925 – Published 21 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021925

Abstract

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.

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Phys. Rev. E 80, 021925– Published 21 August, 2009
  • Received 10 December 2008

© 2009 American Physical Society

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